Viscous Fingering Induced by a pH-Sensitive Clock Reaction

Electroconvective viscous fingering in a single polyelectrolyte fluid on a charge selective surface

When a low-viscosity fluid displaces into a higher-viscosity fluid, the liquid-liquid interface becomes unstable causing finger-like patterns. This viscous fingering instability has been widely observed in nature and engineering systems with two adjoined fluids. Here, we demonstrate a hitherto-unrealizable viscous fingering in a single fluid-solid interface. In a single polyelectrolyte fluid on a charge selective surface, selective ion rejection through the surface initiates i) stepwise ion concentration and viscosity gradient boundaries in the fluid and ii) electroconvective vortices on the surface. As the vortices grow, the viscosity gradient boundary pushes away from the surface, resulting viscous fingering. Comparable to conventional one with two fluids, i) a viscosity ratio ([Formula: see text]) governs the onset of this electroconvective viscous fingering, and ii) the boundary properties (finger velocity and rheological effects) - represented by [Formula: see text], electric Rayleigh ([Formula: see text]), Schmidt ([Formula: see text]), and Deborah ([Formula: see text]) numbers - determine finger shapes (straight v.s. ramified, the onset length of fingering, and relative finger width). With controllable onset and shape, the mechanism of electroconvective viscous fingering offers new possibilities for manipulating ion transport and dendritic instability in electrochemical systems.

Influence of Oxygen on Chemoconvective Patterns in the Iodine Clock Reaction

There is increasing interest in using chemical clock reactions to drive material formation; however, these reactions are often subject to chemoconvective effects, and control of such systems remains challenging. Here, we show how the transfer of oxygen at the air-water interface plays a crucial role in the spatiotemporal behavior of the iodine clock reaction with sulfite. A kinetic model was developed to demonstrate how the reaction of oxygen with sulfite can control a switch from a low-iodine to high-iodine state under well-stirred conditions and drive the formation of transient iodine gradients in unstirred solutions. In experiments in thin layers with optimal depths, the reaction couples with convective instability at the air-water interface forming an extended network-like structure of iodine at the surface that develops into a spotted pattern at the base of the layer. Thus, oxygen drives the spatial separation of iodine states essential for patterns in this system and may influence pattern selection in other clock reaction systems with sulfite.

Stabilization of periodically forced Hele-Shaw flows by means of a nonmonotonic viscosity profile

The onset of viscous fingering in the presence of a viscosity profile is investigated theoretically for two immiscible fluids undergoing a time-dependent injection. Here, we show that the presence of a positive viscosity gradient at the interface between both fluids stabilizes the interface facilitating the spread of the perturbation. This effect is much more pronounced in the case of sinusoidal injection flows. The influence of the viscosity gradient on the dispersion relation is analyzed. Numerical simulations of the Navier-Stokes equation confirm the linear stability analysis.

A bottom-up approach to construct or deconstruct a fluid instability

Fluid instabilities have been the subject of study for a long time. Despite all the extensive knowledge, they still constitute a serious challenge for many industrial applications. Here, we experimentally consider an interface between two fluids with different viscosities and analyze their relative displacement. We designed the contents of each fluid in such a way that a chemical reaction takes place at the interface and use this reaction to suppress or induce a fingering instability at will. This process describes a road map to control viscous fingering instabilities in more complex systems via interfacial chemical reactions.

Anomalous patterns of Saffman-Taylor fingering instability during a metastable phase separation

Phase separation is important in biology, biochemistry, industry, and other areas and is divided into two types: a spinodal decomposition type and a nucleation and growth type. The spinodal decomposition type phase separation occurs under the thermodynamically unstable conditions, and the nucleation and growth type phase separation occurs under thermodynamically metastable conditions. On the other hand, when a less viscous fluid displaces a more viscous one in porous media, the interface of the two fluids becomes hydrodynamically unstable and forms a finger-like pattern. The coupling of the hydrodynamic instability with the thermodynamic instability has been studied. It is reported that the hydrodynamic instability under thermodynamically unstable conditions, where spinodal decomposition type phase separation occurs, creates multiple moving droplets with a radius of 3-4 mm because of the spontaneous convection induced by the Korteweg force, which is driven by a compositional gradient during phase separation. However, the hydrodynamic instability under metastable conditions, where the phase separation of nucleation and growth type occurs, is still unrevealed. In this study, we applied fingering instability (hydrodynamic instability) under the metastable conditions, where the patterns are changed from fingering or droplets to anomalous patterns such as tip-widening or needle-like (top-pointed) fingering patterns when the initial concentration is metastable, which is considered near a binodal curve. These patterns are ubiquitous in nature, similar to dendrite crystals (snowflakes) or our body's cells. Thus, the patterns created can be controlled through hydrodynamic conditions such as the injection flow and thermodynamic conditions such as spinodal decomposition (thermodynamically unstable conditions) and metastable conditions.

Highly viscous fluid displaced by a chemically controlled reactive interface

Displacement of a viscous fluid by a less viscous one is a challenging problem that usually involves the formation of interfacial digitations propagating into each one of the fluids, mixing them and preventing their normal displacement. We propose in this manuscript a protocol that is implemented via numerical simulation of the corresponding equations to improve the efficiency of the displacement. We consider a chemically active interface between the two chemically active fluids that produce a large viscosity interface that facilitates the process. All the relevant parameters of the mechanism are numerically analyzed aiming to optimize the efficiency of the method.

Criterion for Fingering Instabilities in Colloidal Gels

We sandwich a colloidal gel between two parallel plates and induce a radial flow by lifting the upper plate at a constant velocity. Two distinct scenarios result from such a tensile test: (i) stable flows during which the gel undergoes a tensile deformation without yielding, and (ii) unstable flows characterized by the radial growth of air fingers into the gel. We show that the unstable regime occurs beyond a critical energy input, independent of the gel's macroscopic yield stress. This implies a local fluidization of the gel at the tip of the growing fingers and results in the most unstable wavelength of the patterns exhibiting the characteristic scalings of the classical viscous fingering instability. Our work provides a quantitative criterion for the onset of fingering in colloidal gels based on a local shear-induced yielding in agreement with the delayed failure framework.

Reaction-driven oscillating viscous fingering

Localized oscillations can develop thanks to the interplay of reaction and diffusion processes when two reactants A and B of an oscillating reaction are placed in contact, meet by diffusion, and react. We study numerically the properties of such an A+B→ oscillator configuration using the Brusselator model. The influence of a hydrodynamic viscous fingering instability on localized concentration oscillations is next analyzed when the oscillating chemical reaction changes the viscosity of the solutions involved. Nonlinear simulations of the related reaction-diffusion-convection equations with the fluid viscosity varying with the concentration of an intermediate oscillatory species show an active coupling between the oscillatory kinetics and the viscously driven instability. The periodic oscillations in the concentration of the intermediate species induce localized changes in the viscosity, which in turn can affect the fingering instability. We show that the oscillating kinetics can also trigger viscous fingering in an initially viscously stable displacement, while localized changes in the viscosity profile can induce oscillations in an initially nonoscillating reactive system.